Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations
type: Item
instance of: scholarly article
title: Generic solvability of the axisymmetric 3-D Euler equations and the 2-D Boussinesq equations
zbMATH Open document ID: 0939.35149
published in: Journal of Differential Equations
publication date: 1999-10-25T00:00:00Z
review text: Using a new criterion for finite-time blow-up of a smooth axisymmetric solutions to incompressible Euler equations, the authors prove global existence of smooth axisymmetric solutions in a domain of cylindrical type, which can be the whole \(\mathbb{R}^3\). Then using this results, the authors establish the solvability of Euler equations in cylindrical domains which do not contain the axis of symmetry. Similar results are also proved for two-dimensional Boussinesq system.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76B03
zbMATH DE Number: 1339355
zbMATH Keywords: finite-time blow-up
zbMATH Keywords: smooth axisymmetric solutions
zbMATH Keywords: incompressible Euler equations
zbMATH Keywords: global existence
zbMATH Keywords: cylindrical domains
zbMATH Keywords: two-dimensional Boussinesq system
author: Dongho Chae
author: O. Yu. Imanuvilov
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3607
OpenAlex ID: W1999939630
cites work: Remarks on the breakdown of smooth solutions for the 3-D Euler equations
cites work: On the breakdown of axisymmetric smooth solutions for the 3-D Euler equations
cites work: Local existence and blow-up criterion for the Boussinesq equations
cites work: Geometric Statistics in Turbulence
cites work: On the blow-up of solutions of the 3-D Euler equations in a bounded domain
cites work: Q3937706
cites work: Nonstationary flows of viscous and ideal fluids in \(R^3\)
cites work: On classical solutions of the two-dimensional non-stationary Euler equation
cites work: Q5628582
cites work: Vorticity and the mathematical theory of incompressible fluid flow
cites work: Remarks on axisymmetric solutions of the incompressible euler system
cites work: A continuation principle for the 3-D Euler equations for incompressible fluids in a bounded domain
cites work: Note on global existence for axially symmetric solutions of the Euler system
DOI: 10.1006/JDEQ.1998.3607
description: scientific article; zbMATH DE number 1339355